BAGHDAD (Reuters) - Iraqi Prime Minister Haider al-Abadi on Friday ordered security forces to ease access to Baghdad's fortified Green Zone and main streets, in an apparent bid to improve daily life for ordinary Iraqis as fresh protests erupted across the country.

The capital and many southern cities have witnessed demonstrations in recent weeks calling for provision of basic services, the trial of corrupt politicians, and the shakeup of a system riddled with graft and incompetence.

Tens of thousands of demonstrators filled Baghdad's Tahrir Square on Friday in what a senior security official called the biggest protest of the summer. Thousands more rallied in Najaf, Basra and other cities across the Shi'ite southern heartland following a call from powerful Shi'ite cleric Moqtada al-Sadr.

Protesters' demands, which initially aimed at improving power supply amid a sweltering heatwave, have focused more on encouraging Abadi to accelerate reforms, put corrupt officials on trial and loosen the grip of powerful parties over the state.

"What Abadi has done so far is just casual reform. It's not the real reforms that most of the Iraqis are looking for," said Mazen al-Ushaiqer, a civil society leader at the Baghdad rally. "He is trying very hard but we think he can try harder."

Partly in response to protests earlier this month, Abadi began pushing reforms to a system he says has deprived Iraqis of basic services and undermined the fight against Islamic State militants.

He announced several measures to combat corruption and mismanagement including scrapping layers of senior government posts, cutting security details and other perks for officials, and encouraging corruption investigations.

On Friday, he directed military commanders to ease civilian access to the Green Zone, the central Baghdad district home to many government buildings and several Western embassies.

The 10-square-kilometre area on the bank of the Tigris River once housed the headquarters of the U.S. occupation and before that one of Saddam Hussein's republican palaces.

Checkpoints and concrete barriers have blocked bridges and highways leading to the neighborhood for years, symbolizing the isolation of Iraq's leadership from its people and wreaking havoc on traffic in the city of 7 million people.

Abadi also ordered the elimination of no-go zones set up by militias and political parties in Baghdad and other cities in response to more than a decade of car bombings.

SECURITY CONCERNS

Friday's edicts showed that security remains a high priority. Abadi called for a plan "to protect civilians ... from being targeted by terrorism", according to online statements, but did not identify specific measures or a timeline.

Though he has managed to reduce the army's security role in the city and lifted a nighttime curfew, movement in many areas remains constrained by blast walls despite a pledge in November to remove them.

Bomb attacks, many of them claimed by Islamic State, continue to strike the Iraqi capital.

At least six people were killed on Friday morning in a car bomb attack in the southern district of Zafaraniyah, police and medical sources said. Islamic State insurgents, who control large swathes of the country's north and west, said in an online statement they were behind the blast at a police headquarters.

Security at Friday's protests was tight and helicopters circled overhead. At the Baghdad protest at least four people were wounded in clashes and security forces detained a handful of youths carrying weapons.

Hamid Mutlak, a member of parliament's security committee, warned against unnamed elements he said wanted to undermine the momentum towards reform and urged Abadi to take decisive action.

"Mr Abadi should be clear, candid, precise and brave," Mutlak told Al Arabiya television. "He should name the corrupt people, refer them to the judiciary and sack them."

"PREVIOUS PROMISES"

Abadi ordered on Friday the formation of a legal committee to review the ownership of state properties and return illegally gained assets to the state. Critics say some officials have abused their authority to appropriate state-owned properties for personal use.

Top Shi'ite cleric Grand Ayatollah Ali al-Sistani, who wields authority few Iraqi politicians would openly challenge, has called on Abadi to "strike with an iron fist" against corruption.

On Friday, he cautioned protesters against letting personal goals distract from their demands while urging politicians to provide tangible results of reform measures.

"The citizens have tried previous promises and found nothing in reality that would solve the problems they have suffered from for so long. They saw that these promises were only aimed at temporarily relieving their suffering," Sistani said in a sermon delivered by a spokesman.

The provincial governors of Muthanna and Qadisiya, in Iraq's oil-producing south, offered to resign on Friday, local officials said, following allegations of administrative and financial wrongdoing. It was not immediately clear when they would leave their posts.